Change name, then get domain?

I am sorry if this is a repost–I thought I already did this but I can’t find it now!

I would like to get my own domain name, but at the same time, I think I would like to change the name of my blog. But I am just wondering about redirecting traffic. And, when I go to register my domain, there isn’t an option to change the name there. So, I am assuming I would need to change it first, and then upgrade to my own domain. But what happens when someone tries to find my blog?

In order to map to a domain one must have an underlying .wordpress.com subdomain blog to map from. If you have registered a .wordpress.com blog you log in under the exact same username account that registered the blog and purchase a domain name by purchasing an annually renewable domain mapping upgrade for the blog. http://en.support.wordpress.com/domains/

Dashboard > Store > My Upgrades is where you do the primary blog set up knowing it can take between 24 – 72 hours for domain name propagation to take place throughout the internet. You can view the DNS changes here > http://www.whatsmydns.net/ What’s important during that stage is to be patient.

But am I at a disadvantage in not having a site title and URL that match?

No. Wheter or not the two are the same is irrelevant. All traffic will be seamlessly redirected from any .wordpress.com link they click anywhere on the internet to the same content under the new domain URL.

Timethief, thanks so much. I think I am getting a glimmer of understanding (sorry–I sometimes feel debilitatingly right brained). So, can I go through a scenario with you? Right now my url says damommacheftravels.wordpress.com. Damommachef Travels was also the title of my blog. Now that I am getting more serious about it, I want to change the title of my blog to The Traveling Humanist (which I already did, actually). I would like to show readers that I am serious, and would like to get rid of the wordpress word in the url. But at the same time, I would like the URL to say TheTravelingHumanist.com. So I guess my question is:
–Is this a good idea?
–Do I just make this a sub-domain that would then go to the damommacheftravels original wordpress url I set up?
Thanks again, and sorry I am so slow.